Information processing apparatus, information processing method, and non-transitory computer readable medium

ABSTRACT

According to one embodiment, an information processing apparatus includes: a processor configured to select a first case based on subject data including at least one feature, and acquire a first prediction value that is a value of an objective variable included in the first case; a first estimator configured to estimate frequency data indicating frequencies of observation values of the objective variable, based on a history of observation values of the objective variable; a second estimator configured to estimate first frequency data indicating frequencies of first prediction values, based on a history of first prediction values acquired before the first prediction value is acquired; and a corrector configured to correct the first prediction value acquired by the processor, based on the frequency data and the first frequency data.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromthe prior Japanese Patent Application No. 2020-150029, filed on Sep. 7,2020, the entire contents of which are incorporated herein by reference.

FIELD

Embodiments described herein relate to an information processingapparatus, an information processing method, and a computer program.

BACKGROUND

When numerical prediction of a variable (which will be referred to as anobjective variable) is performed, in general, a model for prediction iscreated. As one of methods for creating such a model, prediction isperformed based on search for past similar examples in some cases. Forexample, using a given current state, a plurality of similar cases(similar examples) are selected from a database in which past cases arestored. Each case includes a state and a value of the objectivevariable, and a plurality of similar examples are selected that rankhighly in terms of closeness of distance to the current state. Adistribution of the values of the objective variable included in theselected similar examples is outputted as probabilistic predictions.However, when distances between the selected similar examples and thecurrent state are large, the outputted distribution significantlydeviates from an intended distribution of prediction values, andprediction performance is reduced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a prediction apparatus that is aninformation processing apparatus according to a first embodiment;

FIG. 2 shows an example of a past state DB;

FIG. 3 shows an example of selection of similar examples in a featurespace;

FIG. 4 is a block diagram of a prediction corrector;

FIG. 5 is a block diagram of a member corrector;

FIG. 6 is a diagram for describing correction performed by a frequencydistribution corrector;

FIG. 7 is a flowchart of an example of operation of the predictionapparatus according to the first embodiment;

FIG. 8 is a block diagram of a prediction corrector in the predictionapparatus, according to a second embodiment;

FIG. 9 is a block diagram of a member corrector according to the secondembodiment;

FIG. 10 is a diagram for describing correction performed by a constraintcorrector 34;

FIG. 11 is a block diagram of a prediction apparatus according to athird embodiment;

FIG. 12 is a block diagram of a periodicity extractor;

FIG. 13 is a block diagram of a prediction apparatus according to afourth embodiment;

FIG. 14 is a flowchart of an example of operation of the predictionapparatus according to the fourth embodiment;

FIG. 15 is a block diagram of a prediction apparatus according to afifth embodiment;

FIG. 16 shows an example of a past numerically calculated feature DB;and

FIG. 17 shows a hardware configuration of any of the predictionapparatuses (information processing apparatuses) according to theembodiments.

DETAILED DESCRIPTION

According to one embodiment, an information processing apparatusincludes: a processor configured to select a first case based on subjectdata including at least one feature, and acquire a first predictionvalue that is a value of an objective variable included in the firstcase; a first estimator configured to estimate frequency data indicatingfrequencies of observation values of the objective variable, based on ahistory of observation values of the objective variable; a secondestimator configured to estimate first frequency data indicatingfrequencies of first prediction values, based on a history of firstprediction values acquired before the first prediction value isacquired; and a corrector configured to correct the first predictionvalue acquired by the processor, based on the frequency data and thefirst frequency data.

Hereinafter, embodiments of the present invention will be described withreference to drawings. In the following, a description will be given bytaking weather prediction, particularly prediction of solar irradianceat a certain point A, as an example. However, the embodiments can beapplied to various prediction, and is not limited to weather prediction.Prediction may be prediction of anything, such as prediction of demandfor electric power, prediction of share prices on a stock market,prediction of prices of electricity on an electricity transactionmarket, or prediction of a meteorological variable other than the solarirradiance.

First Embodiment

FIG. 1 is a block diagram of a prediction apparatus 101 that is aninformation processing apparatus according to a first embodiment. Theprediction apparatus 101 in FIG. 1 includes a past state database (DB)11, a similar example selector (processor) 12, a state acquirer 13, anobjective variable acquirer 14, a prediction corrector 15, and an outputdevice 16. The state acquirer 13 is communicably connected to a stateobservation device 201. The objective variable acquirer 14 iscommunicably connected to an objective variable observation device 202.

[Past State DB 11]

The past state DB 11 stores a plurality of cases, each of which includesstate data (first data) on a subject system and a value of an objectivevariable, each in association with a time. A set of state data, a valueof the objective variable, and a time corresponds to one case. The valueof the objective variable is a past observation value corresponding to astate indicated by the state data, and is used for a future predictionvalue corresponding to the state.

The state data (first data) on the subject system includes one or morefeatures that characterize a state of the subject system. For example,the state data includes meteorological variables such as a temperature,a humidity, and a wind speed at the point A at a certain time, as a pastweather state (past features). To be more general, the state data mayinclude other meteorological variables and the like.

The objective variable is a feature related to a past weather state, andis a feature to be predicted in the present embodiment. In the presentembodiment, the objective variable is assumed to be solar irradiance atthe point A on a next day, that is, 24 hours later. Assuming that a timeof state data corresponding to a value of the objective variable is “t”,the value of the objective variable corresponding to the state data (thevalue of the objective variable included in the same case that includesthe state data) is not solar irradiance at the point A at the time “t”,but solar irradiance at the point A 24 hours after “t”.

Although the features are meteorological variables at the point A in thepresent example, features at points around the point A can also beadded, on a supposition that the meteorological variables at such nearbypoints also affect the solar irradiance. Similarly, the meteorologicalvariables before the time of prediction (before the time “t”) can alsobe added as features.

FIG. 2 shows an example of the past state DB 11. In the past state DB11, a plurality of past several years of cases, each of which is a setof state data (one or more features) and a value of the objectivevariable as described above, are stored for each time.

[State Acquirer 13]

The state acquirer 13 acquires, from the state observation device 201,state data including one or more features of the same types as thefeatures in the past state DB 11. As an example, the state acquirer 13acquires state data including a temperature, a humidity, an atmosphericpressure, a wind speed, and the like at each fixed interval. Forexample, the state observation device 201 is installed at the point A,and observes a temperature, a humidity, an atmospheric pressure, a windspeed, and the like at the point A. The state acquirer 13 stores theacquired state data as a history in an internal storage. The stateacquirer 13 provides, to the similar example selector 12, current statedata (subject data) that is state data at a time the similar exampleselector 12 uses the state data for prediction. The current state data(subject data) may be provided in response to a request from the similarexample selector 12. The current state data includes one or morefeatures at the current time, that is, the time at which prediction isintended to be performed. The current state data is a feature orfeatures of the same types as the features stored in the past state DB11. In the above-described example, the current state data includes atemperature, a humidity, an atmospheric pressure, a wind speed, and thelike at the current time at the point A.

[Similar Example Selector 12]

The similar example selector 12 (processor) determines that predictionof the objective variable is performed at each predetermined time, andreceives current state data to be used for prediction from the stateacquirer 13.

The similar example selector 12 calculates a degree of similaritybetween the state data (one or more features) stored in the past stateDB 11 and the current state data, in a feature space that is a spacewith each feature serving as a coordinate of a coordinate system. Thedegree of similarity is calculated based on a predetermined distance(metric) that indicates a degree of closeness in the feature space.Typically, the degree of similarity is measured as a Euclidean distancein the feature space. In such a case, a shorter distance indicates moresimilarity.

Assuming that the Euclidean distance between sets of the features“X”=(x₁, . . . , x_(N)) and “Y”=(y₁, . . . , y_(N)) is “d”, theEuclidean distance is calculated as follows:

[Expression 1]

d=√{square root over (Σ_(i=1) ^(N)(x_(i)−y_(i))²)}  (1)

Since the features include features of different dimensions and featuresof different scales, such as temperature, wind speed, and atmosphericpressure, it is preferable that appropriate standardization be madebeforehand.

The similar example selector 12 selects a predetermined number (M) ofcases in descending order of degree of similarity (ascending order ofdistance, or ascending order of value as the degree of similarity). Theselected cases are referred to as similar examples or similar cases.

FIG. 3 shows an example of selection of similar examples in a featurespace in which a plurality of the features are assumed to be a feature 1and a feature 2. A point C in the center corresponds to current statedata, and points 1, 2, 3, . . . , M correspond to similar examples.

A whole of the selected similar examples is referred to as an ensemble,and “M” is referred to as a size of the ensemble. Each case in theensemble is referred to as a member. The members have member rankingsthat indicate what place a member ranks in descending order of degree ofsimilarity. In the example in FIG. 3, since the points 1, 2, 3, . . . ,M, in this order, are closer to the current state data, the cases 1 toM, in this order, have higher rankings.

The similar example selector 12 acquires respective values of theobjective variable in the selected similar examples, as predictionvalues of the objective variable corresponding to the current statedata. A set of the prediction values is referred to as ensembleprediction data. Each prediction value in the ensemble prediction datais also referred to as an ensemble member. Each member value is aprediction value of the objective variable. Dispersion of such valuescan be regarded as uncertainty of the prediction, and the ensembleprediction data that is a whole of the prediction values can be regardedas probabilistic predictions. In other words, the ensemble predictiondata is probabilistic predictions based on a set of a plurality of theprediction values.

Hereinafter, a prediction value of a member with a ranking “k” at a time“t” is denoted by “p_(k) ^((t))”. The ensemble prediction data can bedenoted by {p₁ ^((t)), p₂ ^((t)), . . . , p_(M) ^((t))}.

As described above, the similar example selector 12 corresponds to aprocessor that selects a similar example from among a plurality ofcases, based on current state data, and acquires a prediction value thatis a value of the objective variable included in the selected similarexample.

[Objective Variable Acquirer 14]

The objective variable acquirer 14 acquires, from the objective variableobservation device 202, an observation value of the objective variablethat is to be predicted, at each fixed time interval. In other words,the objective variable acquirer 14 collects observation values of theobjective variable that is to be predicted, from the objective variableobservation device 202. In the example of the present embodiment, thesolar irradiance at the point A is the objective variable. The objectivevariable observation device 202 such as an instrument for measuringsolar irradiance is installed at the point A, and the objective variableacquirer 14 collects values of the solar irradiance from the objectivevariable observation device 202. The objective variable acquirer 14 maystore the collected observation values of the objective variable as ahistory in an internal storage. The objective variable acquirer 14provides the collected observation values of the objective variable tothe prediction corrector 15. The observation values of the objectivevariable may be provided in response to a request from the predictioncorrector 15. The objective variable is an objective variable of thesame type as a feature stored in past state DB 11.

The observation values of the objective variable collected by theobjective variable acquirer 14 and the state data acquired by the stateacquirer 13 may be accumulated in the past state DB 11. In such a case,the similar example selector 12 may acquire current state data from thepast state DB 11, and the prediction corrector 15 may acquire anobservation value of the objective variable from the past state DB 11.

[Prediction Corrector 15]

The prediction corrector 15 corrects the ensemble prediction dataprovided from the similar example selector 12. More specifically, theprediction corrector 15 corrects the individual prediction values “p₁^((t))”, “p₂ ^((t))”, . . . , “p_(M) ^((t))” included in the ensembleprediction data, and provides corrected prediction values “q₁ ^((t))”,“q₂ ^((t))”, . . . , “q_(M) ^((t))” to the output device 16.

FIG. 4 is a block diagram of the prediction corrector 15. The predictioncorrector 15 includes an objective variable cumulative distributionfunction estimator 21 (first estimator) 21 and member correctors 1 to M.

[Objective Variable Cumulative Distribution Function Estimator 21]

The objective variable cumulative distribution function estimator 21estimates data (frequency data) related to frequency of the observationvalues of the objective variable, based on the observation values of theobjective variable provided from the objective variable acquirer 14.Specifically, a cumulative distribution function “F^((t))” for theobservation values of the objective variable is estimated as thefrequency data.

There are various methods for estimating a cumulative distributionfunction from data acquired with respect to a variable. In the presentembodiment, a following method is used as an example. It is assumed thatat present, there are N values “x₁”, “x₂”, . . . , “x_(N)” that arecollected over a certain time period with respect to a variable “X”. Atthe time, an estimation expression for a cumulative distributionfunction “P(X)” for “X” is given as follows:

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 2} \right\rbrack & \; \\{{P(X)} = {\frac{1}{N}\Sigma_{i = 1}^{N}{\theta\left( {X - x_{i}} \right)}}} & (2)\end{matrix}$

where θ is a function referred to as Heaviside step function, and isdefined by a following expression:

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 3} \right\rbrack & \; \\{{\theta(x)} = \left\{ \begin{matrix}1 & {x \geq 0} \\0 & {x < 0}\end{matrix} \right.} & (3)\end{matrix}$

In the present embodiment, estimation of the cumulative distributionfunction is performed by using data (observation values of the objectivevariable) collected during a predetermined time period “L”, that is,between “t−L” and “t−1” assuming that a current time is “t”. In a caseof weather prediction, a length of “L” is, as an example, approximatelythree months. Such a time period corresponds to a length of one seasonin Japan. Although a cumulative distribution function is estimated asthe frequency data, a probability density distribution, a histogram, orthe like may also be estimated.

[Member Correctors 1 to M]

Each member corrector k (k=1 to M) corrects the prediction value “p_(k)^((t))” of a member with the ranking k, based on the cumulativedistribution function for the observation values of the objectivevariable, and calculates the corrected prediction value “q_(k) ^((t))”.

FIG. 5 is a block diagram of a member corrector k The member corrector kincludes a prediction value cumulative distribution function estimator31 (second estimator) and a frequency distribution corrector 32(corrector).

[Prediction Value Cumulative Distribution Function Estimator 31]

The prediction value cumulative distribution function estimator 31collects the prediction values “p_(k) ^((t))” for an ordinal number “k”for a fixed time period, and generates frequency data on the predictionvalues for the ordinal number “k”. Specifically, a cumulativedistribution function for the prediction values for the ordinal number“k” is estimated as the frequency data. An estimation method and a datacollection period are the same as in the case of the objective variablecumulative distribution function. Although a cumulative distributionfunction is estimated as the frequency data in the present example, aprobability density distribution, a histogram, or the like may also beestimated.

[Frequency Distribution Corrector 32]

The frequency distribution corrector 32 calculates the correctedprediction value “q_(k) ^((t))” for the ordinal number “k” from theprediction value “p_(k) ^((t))” for the ordinal number “k”, by using theobjective variable cumulative distribution function “F^((t))” and theprediction value cumulative distribution function “G_(k) ^((t))” for theordinal number “k”. The frequency distribution corrector 32 calculates acumulative probability (frequency) corresponding to the prediction value“p_(k) ^((t))” (first prediction value), based on the prediction valuecumulative distribution function “G_(k) ^((t))” (frequency data). Then,on the objective variable cumulative distribution function “F^((t))”(the frequency data on the observation values of the objectivevariable), the value “q_(k) ^((t))” corresponding to the calculatedcumulative probability (frequency) is calculated. The first predictionvalue is corrected based on the calculated value. As an example, thecalculated value “q_(k) ^((t))” itself is used for the correctedprediction value. Hereinafter, details will be described by using FIG.6.

FIG. 6 is a diagram for describing the correction performed by thefrequency distribution corrector 32. A horizontal axis shows values ofthe objective variable, and a vertical axis shows values of cumulativedistribution function. Two graphs represent the objective variablecumulative distribution function “F(^(t))” and the prediction valuecumulative distribution function “G_(k) ^((t))”. If prediction valuesare correct, the two cumulative distribution functions are expected tomatch each other. However, the two graphs may possibly differ from eachother in actuality, and such difference between the two graphs leads toa decrease in prediction accuracy. As shown in the drawing, thefrequency distribution corrector 32 determines the corrected predictionvalue “q_(k) ^((t))” such that

F ^((t))(q _(k) ^((t)))=G _(k) ^((t))(p _(k) ^((t)))   (4)

In such a case, “q_(k) ^((t))−p_(k) ^((t))” corresponds to a correctionamount.

Correction can be performed similarly when a probability densitydistribution, a histogram, or the like is used for the frequency data onthe prediction values and the frequency data on the observation values.For example, a frequency or a probability corresponding to theprediction value “p_(k) ^((t))” is identified from the frequency data onthe prediction values, and a value of the objective variablecorresponding to the identified frequency or probability is identifiedfrom the frequency data on the observation values. The identified valueof the objective variable is used for the corrected prediction value“q_(k) ^((t))”.

FIG. 7 is a flowchart of an example of prediction processing performedby the prediction apparatus 101 according to the first embodiment.First, on a supposition that operation of the prediction apparatus 101starts at the time “t”=0, “t” is set to zero (S101), and the similarexample selector 12 calculates the prediction values {p₁ ^((t)), p₂^((t)), . . . , p_(M) ^((t))} before correction (S102). To performcorrection, it is required to accumulate observation values andprediction values of the objective variable during the time period “L”.It is determined whether or not t<L (S103). When t<L, the predictioncorrector 15 outputs {p₁ ^((t)), p₂ ^((t)), . . . , p_(M) ^((t))} asprediction values without correction (S104), on a supposition thatsufficient data is not collected.

When t>=L, the objective variable cumulative distribution functionestimator 21 in the prediction corrector 15 estimates “F^((t))” (S111).Subsequently, it is set that k=1 (S112), and the prediction valuecumulative distribution function estimator 31 in the member corrector kestimates “G_(k) ^((t))” (S113). The frequency distribution corrector 32corrects the prediction value “p_(k) ^((t))” by using “F^((t))” and“G_(k) ^((t))”, and obtains the corrected prediction value “q_(k)^((t))” (S114). One is added to “k” (S115), and while “k” is not largerthan “M” (No in S116), the processing returns to step S112. When thecorrected prediction value “q_(k) ^((t))” is obtained for every memberwith “k”=1, . . . , M (Yes in S116), a set of the corrected predictionvalues from the member correctors 1 to M are transmitted as ensembleprediction data to the output device 16 (S105). The output device 16performs output processing such as displaying the ensemble predictiondata on a screen or transmitting the ensemble prediction data to anotherdevice.

Thereafter, the objective variable acquirer 14 acquires an observationvalue “o^((t))”. Specifically, at a time “t+1”, the objective variableacquirer 14 acquires an observation value (S106, S107). In the exampleof predicting the solar irradiance at the point A on a next day (24hours later), the time “t+1” corresponds to 24 hours later, and solarirradiance observed by the objective variable observation device 202 atthe time 24 hours later is acquired. The prediction processing isrepeated until a termination condition is fulfilled (S108). Examples ofthe termination condition include a case where “t” reaches apredetermined value, a case where an instruction about termination isinputted by an operator of the present apparatus, and the like.

As described above, according to the present embodiment, a set ofprediction values that are values included in a plurality of similarexamples are corrected based on the cumulative distribution function forobservation values of the objective variable, and a set of the correctedprediction values are used for ensemble prediction data, wherebyprediction performance can be enhanced. If the plurality of similarexamples are far from current state data, a distribution of theprediction values differs from an intended distribution of predictionvalues. What is desired to be acquired as a distribution (dispersion) ofprediction values is a dispersion of prediction values from a point ofthe current state data (the point C in FIG. 3) in the feature space. Forexample, even if the exactly same temperature, wind speed, and humidityare observed at the point A, each solar irradiance 24 hours later shouldvary, and what is desired to be known is how the solar irradiance vary.However, since a location of each prediction value is apart from thepoint of the current state data in the feature space, a distribution ofthe prediction values acquired from the feature space is different froman intended distribution of prediction values. The larger ordinal numbera member has, the farther the member is from the point C in the featurespace, and hence the more greatly the distribution of the predictionvalues deviates. In this respect, according to the present embodiment,each prediction value is corrected by using the cumulative distributionfunction for the observation values of the objective variable, wherebythe above-described problem can be solved, and prediction performancecan be enhanced.

Second Embodiment

In the above-described first embodiment, the frequency distributioncorrector 32 acquires L data pieces up until the time point “t”, andestimates the cumulative distribution functions “F^((t))”, “G_(k)^((t))” (k=1, . . . , M). When the time period “L” is short, an errorincluded in the estimated cumulative distribution functions may begreat. In such a case, an error in the correction amount based on thecumulative distribution functions may be great, and may cause a declinein prediction performance. A second embodiment solves such a problem.

FIG. 8 is a block diagram of a prediction corrector 15 in the predictionapparatus 101, according to a second embodiment. A difference from thefirst embodiment shown in FIG. 4 is that an observation value “o^((t))”of the objective variable acquired by the objective variable acquirer 14is also given to the member correctors 1 to M.

FIG. 9 is a block diagram of a member corrector k (k=1 to M) accordingto the second embodiment. A difference from the member corrector in thefirst embodiment shown in FIG. 5 is that a constraint coefficientcalculator 33 and a constraint corrector 34 are added.

[Constraint Coefficient Calculator 33]

The constraint coefficient calculator 33 calculates a cumulativeprobability corresponding to the prediction value “p_(k) ^((t))” (firstprediction value), based on the prediction value cumulative distributionfunction “G_(k) ^((t))” (frequency data). Then, on the objectivevariable cumulative distribution function “F^((t))” (the frequency dataon the observation values of the objective variable), the value “q_(k)^((t))” corresponding to the calculated cumulative probability iscalculated. Based on a difference between the prediction value “p_(k)^((t))” and the value “q_(k) ^((t))”, a coefficient (constraintcoefficient) is calculated. As an example, a performance evaluationindex is calculated based on the difference, and the constraintcoefficient is determined such that the performance evaluation index isoptimized or quasi-optimized. The constraint corrector 34 (corrector)obtains a corrected prediction value “r_(k) ^((t))”, by multiplying thedifference between the prediction value “p_(k) ^((t))” and the value“q_(k) ^((t))” by the constraint coefficient, and adding a resultantvalue of the multiplication to the prediction value “p_(k) ^((t))”, aswill be described later.

As an example, the constraint coefficient calculator 33 calculates theconstraint coefficient by using a method called cross-validation suchthat the predetermined performance evaluation index is optimized. Theconstraint coefficient calculator 33 acquires data {(o^((t−L)), p_(k)^((t−L))), . . . , (o^((t−1)), p_(k) ^((t−1)))} that is formed bypairing observation values {o^((t−L)), . . . , o^((t−1))} and predictionvalues {p_(k) ^((t−L)), . . . , p_(k) ^((t−1))} of the objectivevariable during the past time period “L” from the time point “t”, atwhich prediction is performed, such that an observation value and aprediction value corresponding to the same time make a pair.

In the cross-validation method, data is divided into two sets, namelydata for learning and data for validation. Although there are variousmethods for dividing data, a leave-one-out method, which is relativelycommonly used, is used here. In such a case, the data for validation isonly one pair of an observation value and a prediction value, and thisone pair is assumed to be (o_(v), p_(v)). The remaining “L−1” pairs arethe data for learning, and the data for learning are assumed to be{(o_(l) ⁽¹⁾, p_(l) ⁽¹⁾), . . . , (o_(l) ^((L−1)), p_(l) ^((L−1)))}.

As in the first embodiment, the objective variable cumulativedistribution function estimator 21 calculates an objective variablecumulative distribution function “F_(l)” from the observation values inthe data for learning. Similarly, the prediction value cumulativedistribution function estimator 31 calculates a prediction valuecumulative distribution function “G_(l)” from the prediction values inthe data for learning. By using “F_(l)” and “G_(l)”, a correctedprediction value “q_(v)” is calculated from a prediction value “p_(v)”,through a method similar to the method used by the frequencydistribution corrector 32 in the first embodiment.

The constraint coefficient calculator 33 first assumes a value “α” ofthe constraint coefficient. For example, “α” is selected from a fixedrange (for example, a range between zero and one inclusive). Similarlyto the constraint corrector 34, which will be described later, theconstraint coefficient calculator 33 calculates a corrected predictionvalue “r_(v)”, based on the tentatively determined constraintcoefficient “α”. A prediction error is calculated from this “r_(v)” andthe observation value “o_(v)”, based on a following expression:

e=r _(v) −o _(v)   (5)

In such a manner, one error is obtained. In the leave-one-out method,when there are L pairs of data, division into the data for learning andthe data for validation can be made in L different combinations.Accordingly, L errors can be obtained. It is assumed that theperformance evaluation index to be optimized is, for example, RMSE (RootMean Squared Error). In such a case, by using a set of the obtainederrors, the RMSE can be calculated as follows:

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 4} \right\rbrack & \; \\{{RMSE} = \sqrt{\frac{1}{L}{\sum_{i = 1}^{L}{e_{i}}^{2}}}} & (6)\end{matrix}$

Where “e_(i)” represents an error calculated based on an i-thcombination for division into the data for learning and the data forvalidation. The RMSE depends on the assumed value “α” of the constraintcoefficient. In other words, the RMSE is a function for “α”.Accordingly, “α” that minimizes or quasi-minimizes the RMSE can beselected by repeating calculation while variously changing the value of“α”. Quasi-minimization is, for example, to make the RMSE equal to orsmaller than a threshold value. The value of the constraint coefficientcalculated by the constraint coefficient calculator 33 in the membercorrector k with respect to the time “t” is denoted by “α_(k) ^((t))”.

There are various methods for dividing data into the data for learningand the data for validation, other than the leave-one-out method. Amongcommonly used methods, bootstrapping and the like using random numbersare known (see Bradley Efron and Robert J. Tibshirani, An Introductionto the Bootstrap, Chapman & Hall/CRC, 1993). Moreover, for theperformance evaluation index to be optimized, various indices other thanthe RMSE can be used. CRPS (Continuously Ranked Probability Score) iswell known in particular as a performance evaluation index inprobabilistic prediction schemes (see Hans Hersbach, Decomposition ofthe Continuous Ranked Probability Score for Ensemble Prediction Systems,Weather and Forecasting, Vol. 15, Issue 5, pp. 559-570, 2000).

[Constraint Corrector 34]

The constraint corrector 34 performs correction as described below, byusing the constraint coefficient “α_(k) ^((t))” (0≤α_(k) ^((t))≤1)calculated by the constraint coefficient calculator 33.

FIG. 10 is a diagram for describing the correction performed by theconstraint corrector 34.

First, based on the expression (1), a correction amount “δp_(k) ^((t))”can be calculated based on a following expression:

δp_(k) ^((t)) =q _(k) ^((t)) −p _(k) ^((t))   (7)

By multiplying the correction amount by the constraint coefficient“α_(k) ^((t))” and adding a resultant value of the multiplication to theprediction value “p_(k) ^((t))”, the prediction value “r_(k) ^((t))” iscalculated as follows:

r _(k) ^((t)) =p _(k) ^((t))+α_(k) ^((t)) δp _(k) ^((t))   (8)

Data {r₁ ^((t)), r₂ ^((t)), . . . , r_(M) ^((t))} that is a collectionof the thus obtained prediction values is new ensemble prediction data.

As described above, according to the present embodiment, the correctionamounts (δp_(k) ^((t))=q_(k) ^((t))−p_(k) ^((t))) in the firstembodiment are adjusted by using the constraint coefficients, wherebyprediction performance can be enhanced.

Third Embodiment

In the first embodiment, the prediction corrector 15 collectsobservation values of the objective variable and prediction values ofthe objective variable, and estimates the objective variable cumulativedistribution function and the prediction value cumulative distributionfunction (see FIGS. 4 and 5). However, in some cases, periodicity existsin values of the objective variable, depending on a subject that ispredicted, and collection of observation values of the objectivevariable and prediction values of the objective variable can be omittedby utilizing such periodicity. For example, when a weather phenomenon isa subject, obvious periodicities exist, namely daily periodicity andannual periodicity.

FIG. 11 is a block diagram of a prediction apparatus 101 according to athird embodiment. In comparison with the first embodiment, a periodicityextractor 41, an objective variable cumulative distribution functionestimator 42, and a prediction value cumulative distribution functionestimator 43 are added. The objective variable cumulative distributionfunction estimator 21 and the prediction value cumulative distributionfunction estimator 31 included in the prediction corrector 15 in thefirst embodiment are not required.

[Periodicity Extractor 41]

The periodicity extractor 41 identifies a time period associated with acurrent time (a time of the subject data) as a time period withperiodicity of the current time. For example, the periodicity extractor41 obtains a time period with similarity to the current time, based on aperiodicity given beforehand. For example, it is assumed that thecurrent time is day “d” of year “Y” (“d” is a day of the year). It isassumed that a width of the time period (assumed to be h days) and thenumber of years over which data is traced back (assumed to be n years)are predetermined. In such a case, the periodicity extractor 41 extractssimilar segments as follows. Here, an example is shown where annualperiodicity is utilized.

[day “d−h” of year “Y−1” to day “d+h” of year “Y−1”]

[day “d−h” of year “Y−2” to day “d+h” of year “Y−2”]

. . .

[day “d−h” of year “Y−n” to day “d+h” of year “Y−n”]

The periodicity extractor 41 provides information on the extractedsimilar segments (time periods) to the objective variable cumulativedistribution function estimator 42 and the prediction value cumulativedistribution function estimator 43.

[Objective Variable Cumulative Distribution Function Estimator 42]

The objective variable cumulative distribution function estimator 42extracts, from the past state DB 11, a value of the objective variableincluded in each case belonging to each similar segment provided by theperiodicity extractor 41. In other words, observation values belongingto the similar segments, in a history of values (observation values) ofthe objective variable, are extracted. Based on the extractedobservation values, the objective variable cumulative distributionfunction estimator 42 estimates an objective variable cumulativedistribution function (frequency data on the observation values of theobjective variable), through a method similar to the method used by theobjective variable cumulative distribution function estimator 21 in thefirst embodiment. The estimated objective variable cumulativedistribution function is provided to each member corrector k (k=1 to M)in the prediction corrector 15.

[Prediction Value Cumulative Distribution Function Estimator 43]

The prediction value cumulative distribution function estimator 43calculates a prediction value for each time included in the similarsegments provided by the periodicity extractor 41, individually for eachmember ranking as in the first embodiment, and obtains histories of theprediction values (histories of selection of members (cases) with thesame ranking). Based on the histories of the prediction values, theprediction value cumulative distribution function estimator 43 estimatesprediction value cumulative distribution functions. The prediction valuecumulative distribution functions that are estimated for the memberrankings, respectively, are provided to the frequency distributioncorrectors 32 of the corresponding member correctors k in the predictioncorrector 15.

[Other Examples of Configuration of Periodicity Extractor 41]

When a periodicity is not given beforehand, the periodicity extractor 41analyzes the past state DB 11 and detects a periodicity. The periodicityextractor 41 extracts a similar segment by utilizing the detectedperiodicity.

FIG. 12 is a block diagram of the periodicity extractor 41. Theperiodicity extractor 41 includes a power spectrum calculator 45 and apeak detector 46.

[Power Spectrum Calculator 45]

The power spectrum calculator 45 reads past values of the objectivevariable as time-series data from the past state DB 11, and calculates apower spectrum based on the read time-series data. In other words, thepower spectrum calculator 45 calculates a power spectrum, based on ahistory of observation values of the objective variable. The powerspectrum represents absolute values of amplitude (spectrum component) offrequency components corresponding to the values that change like timeseries. If the power spectrum has a large value at some frequency “ω”,such a fact means that a large number of components of that frequencyare included in the objective variable.

[Peak Detector]

The peak detector 46 performs peak detection based on the powerspectrum, identifies a frequency component “ω” among frequencycomponents included in the peak detected through the peak detection, andidentifies a peak width “Δω”. Based on the identified frequencycomponent ω and peak width “Δω”, a similar segment (time period) isdetermined. The frequency component “ω” is a frequency componentselected from among the frequency components included in the peak. As anexample, the frequency component “ω” is a frequency component with thelargest spectrum component among the frequency components included inthe peak. As another example, a median value or the like of thefrequency components included in the peak may be selected.

Having a peak that includes a large spectrum component corresponding toa first frequency component “ω” suggests that the objective variable hasa periodicity with a period “τ”=2π/ω. The peak width “Δω” relates toprecision of the periodicity. For example, a narrow peak width “Δω”indicates precise periodicity. Accordingly, “Δω” can be thought tosuggest a width of an interval to be set as a similar segment. Here, itis assumed that the width of the interval is “Δτ”=2πΔω/ω². As anexample, following segments are determined as similar segments.

[t−τ−Δτ to t−τ+Δτ]

[t−2τ−Δτ to t−2τ+Δτ]

. . .

[t−nτ−Δτ to t−nτ+Δτ]

As described above, according to the present embodiment, the cumulativedistribution functions are estimated based on periodicity of theobjective variable by using the past state DB 11, whereby collection ofobservation values of the objective variable and prediction values ofthe objective variable can be omitted. Accordingly, after the predictionapparatus starts operation, correction of the prediction values (seeS105 of the flowchart in FIG. 7) can be performed earlier.

Fourth Embodiment

In the first embodiment, the frequency distribution corrector 32 of eachmember corrector corrects the prediction value “p_(k) ^((t))” to “q_(k)^((t))”. The correction amount (p_(k) ^((t))−q_(k) ^((t))) depends on asystem (metric) of measuring a distance in the feature space. There arevarious metrics other than the Euclidean distance used in the firstembodiment. By appropriately selecting a metric, there is a possibilitythat prediction performance can be enhanced.

In a fourth embodiment, a plurality of metrics are preset, andcorrection of prediction values is performed for each metric. For eachmetric, a summed value of correction amounts is calculated, andcorrected prediction values based on a metric for which the smallestsummed value is obtained are adopted. Hereinafter, details of thepresent embodiment will be described.

FIG. 13 is a block diagram of a prediction apparatus 101 in the fourthembodiment. In comparison with the prediction apparatus in the firstembodiment, a metric setter 51 and a prediction selector 53 (setselector) are added. Moreover, N pairs of similar example selectors 12and prediction correctors 15 are included. In other words, a pair of asimilar example selector 12_1 and a prediction corrector 15_1 to a pairof a similar example selector 12_N and a prediction corrector 15_N areincluded. For the N pairs, correction amount totalizers 52_1 to 52_N areprovided, respectively.

[Metric Setter 51]

The metric setter 51 sets metrics to be used by the similar exampleselectors 12_1 to 12_N (presented as metrics 1 to N, respectively).

In the present embodiment, an example is shown where a weighted distanceis used for a metric. In such a case, for each of the metrics 1 to N, aweight for each feature is inputted.

Assuming that a weighted distance between sets of features “X”=(x₁, . .. , x_(N)) and “Y”=(y₁, . . . , y_(N)) is “d”, the weighted distance iscalculated as follows:

[Expression 9]

d=√{square root over (Σ_(i=1) ^(N) w _(i)(x _(i) −y _(i))²)}  (9)

Where “w_(i)” is a weight for an i-th feature, and a feature with alarger value of “w_(i)” is deemed to be of greater importance incalculation. The various metrics 1 to N are configured by variouslychanging the value of “w_(i)”.

The similar example selectors 12_1 to 12_N and the prediction correctors15_1 to 15_N operate as in the first embodiment, except that metricsused by the similar example selectors 12_1 to 12_N are different. Inother words, the similar example selectors 12_1 to 12_N select similarexamples by using mutually different metrics. The prediction correctors15_1 to 15_N correct prediction values that are values of the objectivevariable included in the similar examples selected by the similarexample selectors 12_1 to 12_N.

[Correction Amount Totalizers 52_1 to 52_N]

The correction amount totalizers 52_1 to 52_N sum (or total) thecorrection amounts δp_(k) ^((t)) for correction performed by thefrequency distribution correctors 32_1 to 32_N in the predictioncorrector 15_1 to 15_N. For example, assuming that a predetermined timeperiod is “R” and a time at which prediction is performed is “t”, a sum“S” of absolute values of the correction amounts in a segment [t−R, t−1]is calculated as follows:

[Expression 9]

S=Σ _(τ=1) ^(R) |δp _(k) ^((t−τ))|  (10)

The thus calculated “S” is a scale that represents a magnitude of thecorrection. Hereinafter, this “S” will be referred to as a correctionamount summed value. A correction amount summed value corresponding to aj-th metric is denoted by “S_(j)”.

In the above-described example, absolute values of the correctionamounts are used when a correction amount summed value is calculated.Apart from the absolute value, an amount that can be a scale of amagnitude of the correction amount, for example, a square of thecorrection amount can also be used.

[Prediction Selector 53]

The prediction selector 53 selects a metric (or a pair of a similarexample selector and a prediction corrector) with which the smallestcorrection amount summed value is obtained. In other words, a metric (ora pair of a similar example selector and a prediction corrector) isselected with which, among the correction amount summed values “S₁”, . .. , “S_(N)”, the smallest “S_(j)” is obtained. A number denoting theselected metric (or pair) is assumed to be “j_(min)”. The predictionselector 53 generates instructional data to instruct that ensembleprediction data from a j_(min)-th prediction corrector 15 (predictioncorrector 15_j_(min)) be selected, and provides the instructional datato the output device 16.

[Output Device 16]

The output device 16, in accordance with the instructional data from theprediction selector 53, outputs the ensemble prediction data from thej_(min)-th prediction corrector 15 (prediction corrector 15_j_(min))among outputs from the N prediction correctors 15.

FIG. 14 is a flowchart of an example of prediction processing performedthe prediction apparatus 101 according to the fourth embodiment. In adescription below, it is assumed that a similar example selector jrepresents a similar example selector 12_j, a prediction corrector jrepresents a prediction corrector 15_j, and a correction amounttotalizer j represents a correction amount totalizer 52_j.

First, it is set that j=1 (S121), the similar example selector jacquires a plurality of prediction values, based on similar cases(S122), and the prediction corrector j corrects the plurality ofprediction values (S123). The correction amount totalizer j calculates acorrection amount summed value S_(j) (S124). One is added to “j” (S125),and steps S122 to S125 are repeated until “j” reaches “N” (S126). When“j” reaches “N”, the prediction selector 53 selects a number j_(min) ofa metric (or a pair of a similar example selector and a predictioncorrector) with which the smallest correction amount summed value S_(j)is obtained (S127). The output device 16 outputs a set of correctedprediction values (ensemble prediction data) from the j_(min)-thprediction corrector 15 (S128).

As described above, according to the present embodiment, predictionvalues are acquired based on a plurality of metrics, the predictionvalues are corrected, and corrected prediction values with which thesmallest summed value of correction amounts is obtained are selected,whereby prediction performance can be enhanced.

Fifth Embodiment

In the first embodiment, for a state (one or more features) of thesubject system, one or more observation values of the subject system ata certain time point are used. For example, in a case of weatherprediction, a temperature, an atmospheric pressure, and the like at apoint of interest correspond to a state of the subject system. However,when a case of predicting the solar irradiance on a next day is taken asan example, an actual solar irradiance on the next day does not alwayswell agree with solar irradiance in a selected case even if a past statethat is similar to current meteorological variables is selected. This isbecause solar irradiance at any point of interest on a next day isdetermined under influence of not only current meteorological variablesat the point of interest but also current meteorological variables in awider area. It is uncertain what meteorological variable at which pointshould be used for comparison, to obtain more desirable similarity.

In view of such circumstances, in a field of weather prediction, atechnique called analog ensemble is known. This technique is based on afact that numerical weather calculation with high prediction performanceis available for weather prediction. According to a basic concept of theanalog ensemble, if numerical weather calculation with high predictionperformance is possible, more desirable similarity can be obtained byselecting similar meteorological variables to meteorological variablesat a target time point of prediction, which are derived by calculationfrom current meteorological variables, than by comparison with thecurrent meteorological variables. The numerical weather calculation doesnot always predict accurate values, but nevertheless past studies showthat the concept of the analog ensemble is effective (see Luca DelleMonache, F Anthony Eckel, Daran L Rife, Badrinath Nagarajan, and KeithSearight, Probabilistic Weather Prediction with an Analog Ensemble,Monthly Weather Review, Vol. 141, Issue 10, pp. 3498-3516, 2013).

The concept of the analog ensemble used for weather prediction can beapplied to situations where numerical calculation or numerical modelsimulation can be used in general. A fifth embodiment embodies aconfiguration that adopts a concept of using numerical calculation.

FIG. 15 is a block diagram of a prediction apparatus 101 according tothe fifth embodiment. In comparison with the first embodiment, anumerical calculator 61, a feature selector 62, and a past numericallycalculated feature DB 63 are added.

[Numerical Calculator 61]

The numerical calculator 61 performs numerical calculation of a state ofthe subject system at a target time point of prediction from data(current state data) indicating a current state of the subject system,based on a numerical calculation model. A plurality of features areobtained through the numerical calculation. The numerical calculator 61performs numerical calculation from a past state (features) of thesubject system stored in the past state DB 11, based on the numericalcalculation model. A plurality of features are obtained through thenumerical calculation.

[Feature Selector 62]

The feature selector 62 selects a feature (numerically calculatedfeature) to be used to acquire a similar example, among the plurality offeatures obtained through the numerical calculation from the past stateDB 11, and stores the selected numerically calculated feature in thepast numerically calculated feature DB 63. The numerically calculatedfeature may be a feature of the same type as the objective variable. Forexample, when prediction of the solar irradiance is taken as an example,the numerically calculated feature may be a value of the solarirradiance. In addition, for example, a numerically calculated featuredeemed to be useful for determination of similarity may be appropriatelyselected and added to the past numerically calculated feature DB 63.

The feature selector 62 selects a feature (numerically calculatedfeature) to be used to acquire a similar example, among the plurality offeatures obtained through the numerical calculation with respect to thecurrent state data. The selected numerically calculated feature (currentnumerically calculated feature) is provided to the similar exampleselector 12. The selected feature may be a feature of the same type asthe feature stored in the past numerically calculated feature DB 63. Ina case of predicting the solar irradiance at the point A on a next dayas an example, when a value of the solar irradiance is stored as anumerically calculated feature in the past numerically calculatedfeature DB 63, a value of the solar irradiance at the point A on a nextday is selected as a numerically calculated feature. In addition,another numerically calculated feature such as a temperature, ahumidity, or the like at the point A on the next day may be selected,depending on contents of the past numerically calculated feature DB 63.

[Past Numerically Calculated Feature DB63]

The past numerically calculated feature DB 63 stores, in a set with avalue of the objective variable, the one or more features (numericallycalculated features) selected by the feature selector 62 among theplurality of features obtained through the numerical calculation fromthe past state DB 11.

FIG. 16 shows an example of the past numerically calculated feature DB63. Numerically calculated features 1 to N are stored in associationwith a time and a value of the objective variable.

The similar example selector 12 operates as in the first embodiment,except that the current state data and the past state DB 11 in the firstembodiment are replaced with the current numerically calculated featureand the past numerically calculated feature DB 63, respectively. Theprediction corrector 15, the objective variable acquirer 14, and theoutput device 16 also operate as in the first embodiment.

As described above, according to the present embodiment, a feature(numerically calculated feature) is calculated through numericalcalculation, whereby prediction performance can be enhanced.

(Hardware Configuration)

FIG. 17 illustrates a hardware configuration of the prediction apparatus(information processing apparatus) 101 according to the presentembodiment. The information processing apparatus 101 according to thepresent embodiment is configured with a computer device 300. Thecomputer device 300 includes a CPU 301, an input interface 302, adisplay device 303, a communication device 304, a main storage device305 and an external storage device 306, and these are connected to eachother with a bus 307.

The CPU (Central Processing Unit) 301 executes a computer program(prediction program) which realizes the above-described respectivefunctional configurations of the information processing apparatus 101 onthe main storage device 305. The computer program may not be a singleprogram but a plurality of programs or a combination of scripts. By theCPU 301 executing the computer program, the respective functionalconfigurations are realized.

The input interface 302 is a circuit for inputting an operation signalfrom the input device such as a keyboard, a mouse and a touch panel, tothe information processing apparatus 101. The input function of theinformation processing apparatus 101 can be constructed on the inputinterface 302.

The display device 303 displays data or information output from theinformation processing apparatus 101. While the display device 303 is,for example, an LCD (Liquid Crystal Display), a CRT (Cathode-Ray Tube),and a PDP (Plasma Display Panel), the display device 303 is not limitedto this. The data or the information output from the computer device 300can be displayed by this display device 303. The output device of theinformation processing apparatus 101 can be constructed on the displaydevice 303.

The communication device 304 is a circuit for the information processingapparatus 101 to communicate with an external device in a wireless orwired manner. Information can be input from the external device via thecommunication device 304. Information input from the external device canbe stored in a DB.

The main storage device 305 stores a program (prediction program) whichrealizes processing of the present embodiment, data required forexecution of the program, data generated by execution of the program,and the like. The program is developed and executed on the main storagedevice 305. While the main storage device 305 is, for example, a RAM, aDRAM and an SRAM, the main storage device 305 is not limited to this.The storage in each embodiment may be constructed on the main storagedevice 305.

The external storage device 306 stores the above-described program, datarequired for execution of the program, data generated by execution ofthe program, and the like. These kinds of program and data are read outto the main storage device 305 upon processing of the presentembodiment. While the external storage device 306 is, for example, ahard disk, an optical disk, a flash memory and a magnetic tape, theexternal storage device 306 is not limited to this. The storage in eachembodiment may be constructed on the external storage device 306.

Note that the above-described program may be installed in the computerdevice 300 in advance or may be stored in a storage medium such as aCD-ROM. Further, the program may be uploaded on the Internet.

Note that the computer device 300 may include one or a plurality of theprocessors 301, the input interfaces 302, the display devices 303, thecommunication devices 304 and the main storage devices 305, orperipheral equipment such as a printer and a scanner may be connected tothe computer device 300.

Further, the information processing apparatus 101 may be configured witha single computer device 300 or may be configured as a system includinga plurality of computer devices 300 which are connected to each other.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the inventions.

1. An information processing apparatus, comprising: a processorconfigured to select a first case based on subject data including atleast one feature, and acquire a first prediction value that is a valueof an objective variable included in the first case; a first estimatorconfigured to estimate frequency data indicating frequencies ofobservation values of the objective variable, based on a history ofobservation values of the objective variable; a second estimatorconfigured to estimate first frequency data indicating frequencies offirst prediction values, based on a history of first prediction valuesacquired before the first prediction value is acquired; and a correctorconfigured to correct the first prediction value acquired by theprocessor, based on the frequency data and the first frequency data. 2.The information processing apparatus according to claim 1, wherein theprocessor is configured to select the first case from among a pluralityof cases, each of which includes a pair of: first data including atleast one feature; and a value of the objective variable.
 3. Theinformation processing apparatus according to claim 2, wherein theprocessor is configured to select the first case, based on a distancebetween the subject data and the first data included in each of theplurality of cases.
 4. The information processing apparatus according toclaim 1, wherein the processor is configured to further select second tok-th cases, and acquire second to k-th prediction values that are valuesof the objective variable included in the second to k-th cases,respectively, the second estimator is configured to estimate second tok-th frequency data indicating frequencies of the second to k-thprediction values, based on histories of the second to k-th predictionvalues, and the corrector is configured to correct the second to k-thprediction values acquired by the processor, based on the frequency dataand the second to k-th frequency data, respectively.
 5. The informationprocessing apparatus according to claim 4, wherein the processor isconfigured to select the first case from among a plurality of cases,each of which includes a pair of first data including at least onefeature and a value of the objective variable, and the first to k-thcases have rankings according to a distance between the first dataincluded in each of the first to k-th cases and the subject data.
 6. Theinformation processing apparatus according to claim 1, wherein thecorrector is configured to calculate a frequency corresponding to thefirst prediction value acquired by the processor, based on the firstfrequency data; calculate an observation value corresponding to thecalculated frequency, on the frequency data; and correct the firstprediction value, based on the calculated observation value.
 7. Theinformation processing apparatus according to claim 6, wherein thecorrector is configured to correct the first prediction value to a valuethat is equal to the calculated observation value.
 8. The informationprocessing apparatus according to claim 6, further comprising anobjective variable acquirer configured to acquire an observation valueof the objective variable, from an observation device that observes theobjective variable, wherein the corrector is configured to calculate acoefficient, based on a difference between the first prediction valueacquired by the processor and the acquired observation value; andcorrect the first prediction value by adding, to the first predictionvalue, a value obtained by multiplying the difference by thecoefficient.
 9. The information processing apparatus according to claim8, wherein the corrector is configured to calculate a performanceevaluation index, based on the difference between the first predictionvalue acquired by the processor and the acquired observation value, anddetermine the coefficient, based on the performance evaluation index.10. The information processing apparatus according to claim 2, whereinthe plurality of cases are associated with a plurality of times,respectively, the processor is configured to select the first case fromcases belonging to a time period associated with a time of the subjectdata, and the first estimator is configured to estimate the frequencydata, based on observation values belonging to the time period in ahistory of observation values of the objective variable.
 11. Theinformation processing apparatus according to claim 10, wherein the timeperiod is a time period based on periodicity of the objective variable.12. The information processing apparatus according to claim 11, furthercomprising: a power spectrum calculator configured to calculate a powerspectrum, based on the history of the observation values of theobjective variable; and a peak detector configured to perform peakdetection, based on the power spectrum, and determine the time period,based on a frequency component included in a peak detected through thepeak detection, and based on a width of the peak.
 13. The informationprocessing apparatus according to claim 2, comprising a plurality ofsets of the processor, the first estimator, the second estimator, andthe corrector, wherein the processors in the plurality of sets eachselect the first case by using different metrics, and the informationprocessing apparatus further comprises: a plurality of correction amounttotalizers configured to sum correction amounts for the first predictionvalues corrected by the correctors, respectively; a set selectorconfigured to select a set from among the plurality of sets, based onsummed values of the correction amounts; and an output device configuredto output the first prediction value corrected by the corrector in theset selected.
 14. The information processing apparatus according toclaim 1, further comprising a feature generator configured to generatethe at least one feature, based on at least one state amount, byperforming numerical calculation based on a numerical calculation model.15. The information processing apparatus according to claim 1, whereinthe frequency data includes a cumulative distribution function forobservation values of the objective variable.
 16. The informationprocessing apparatus according to claim 1, wherein the first frequencydata includes a cumulative distribution function for the firstprediction values.
 17. An information processing method, comprising:selecting a first case based on subject data including at least onefeature, and acquire a first prediction value that is a value of anobjective variable included in the first case; estimating frequency dataindicating frequencies of observation values of the objective variable,based on a history of observation values of the objective variable;estimating first frequency data indicating frequencies of firstprediction values, based on a history of first prediction valuesacquired before the first prediction value is acquired; and correctingthe first prediction value acquired by the processor, based on thefrequency data and the first frequency data.
 18. A non-transitorycomputer readable medium having a computer program stored therein whichcauses a computer to perform processes when executed by the computer,the processes comprising: selecting a first case based on subject dataincluding at least one feature, and acquire a first prediction valuethat is a value of an objective variable included in the first case;estimating frequency data indicating frequencies of observation valuesof the objective variable, based on a history of observation values ofthe objective variable; estimating first frequency data indicatingfrequencies of first prediction values, based on a history of firstprediction values acquired before the first prediction value isacquired; and correcting the first prediction value acquired by theprocessor, based on the frequency data and the first frequency data.